Supplementary Material – Online Appendix
A. Experimental Instructions
Thanks for your participation. This session consists of the main experiment and a questionnaire. I expect the whole thing to take about 30 minutes.
Depending on your decisions and the luck, you will be able to earn money in addition to the $3 guaranteed for your participation.
Please read the following instructions carefully.
NO communication between participants is allowed at any time during the experiment. If you have any questions, please raise your hand and I will come to assist you privately.
Please now turn off your mobile phone and any other electronic devices. These must remain off until you leave this room.
During the experiment, your earnings will be calculated in “tokens.” You will be paid in Singapore dollars at the following conversion rate:
15 tokens = S$1
To ensure anonymity, your decisions in this session are linked to your Participant ID number and at the end of this session you will be paid by Participant ID number. All payments will be put in an envelope. No other participants will see how much you have been paid. Please do not reveal your choices to any other participant in the experiment.
Your Tasks
The main experiment consists of 12 rounds. In each round, you will make a series of decisions on choosing between a lottery and a certain amount of tokens for sure. The following table shows an example of a round.
Each row in the table corresponds to one decision that you will make. For each row, you will choose between “Left” and “Right”. For instance, in Row 1, if you choose “Left”, you will receive x tokens with 50% probability and y tokens with 50% probability; if you choose “Right”, you will receive z1 tokens with certainty. After you make all 13 decisions in the table and click “Continue”, you will proceed to the next round. The completion of the 12th round entails the end of the experiment. In the experiment, x, y and z will be assigned real values. Note that Left Options differ across rounds; and for each round, Right Options differ across rows. So please read carefully the options presented to you when making decisions.
Left / Right / Decision1 / You have 50% chance winning x tokens and 50% chance winning y tokens / You will receive z1 tokens for sure / Left Right
2 / You have 50% chance winning x tokens and 50% chance winning y tokens / You will receive z2 tokens for sure / Left Right
3 / You have 50% chance winning x tokens and 50% chance winning y tokens / You will receive z3 tokens for sure / Left Right
4 / You have 50% chance winning x tokens and 50% chance winning y tokens / You will receive z4 tokens for sure / Left Right
5 / You have 50% chance winning x tokens and 50% chance winning y tokens / You will receive z5 tokens for sure / Left Right
6 / You have 50% chance winning x tokens and 50% chance winning y tokens / You will receive z6 tokens for sure / Left Right
7 / You have 50% chance winning x tokens and 50% chance winning y tokens / You will receive z7 tokens for sure / Left Right
8 / You have 50% chance winning x tokens and 50% chance winning y tokens / You will receive z8 tokens for sure / Left Right
9 / You have 50% chance winning x tokens and 50% chance winning y tokens / You will receive z9 tokens for sure / Left Right
10 / You have 50% chance winning x tokens and 50% chance winning y tokens / You will receive z10 tokens for sure / Left Right
11 / You have 50% chance winning x tokens and 50% chance winning y tokens / You will receive z11 tokens for sure / Left Right
12 / You have 50% chance winning x tokens and 50% chance winning y tokens / You will receive z12 tokens for sure / Left Right
13 / You have 50% chance winning x tokens and 50% chance winning y tokens / You will receive z13 tokens for sure / Left Right
Your Payment
After you finish your decisions in all the 12 rounds, one round will be randomly selected as the payment round. For this randomly selected round, you will be paid by your decisions in one randomly selected row. Suppose Row 1 is chosen for payment. If you choose Right in Row 1, you will receive z1 tokens for sure. If you choose Left in Row 1, you will receive either x tokens or y tokens with equal probability. The computer will randomly determine the outcome for this lottery.
The earnings will be transformed to Singapore dollars using the 15 tokens=S$1 conversion rate and be paid to you in addition to the S$3 participation fee.
B. Main decision-making task (HM treatment)
In this section, we show all 12 rounds of the main decision-making task in the HM treatment. Note that the order of the six lotteries within the first half of the task is randomized; so is the order of the six lotteries in the second half. The main decision-making tasks in the other treatment conditions are available upon request.
1st round
2nd round
3rd round
4th round
5th round
6th round
7th round
8th round
9th round
10th round
11th round
12th round
C.Additional Discussions on Table 5
In this Appendix, we discuss some additional regression results from Table 5, including the magnitude of the treatment effect.
The coefficients of PriorRisk capture the effect of prior exposure to risk on individuals’ willingness to take risk, while the coefficients of x capture the effect of the “present” lottery risk. We can thus compare the relative importance of these two factors. The coefficients of xare about 0.02 across different specifications and statistically significant, implying that one unit increase of standard deviation in the present lottery increases the number of Safe choices by 0.02. The coefficients of PriorRisk imply that 85 units of increase in standard deviation in the previous lotteries will on average lead an individual to choose additional 0.5 Safe choices. A simple calculation suggests that the magnitude of the effect of prior risk is thus roughly 30% of the effect of present risk.
We also found several secondary results from Table 5. First, the coefficients of the period dummy variables in columns (1)-(3) and the coefficient of Last-3 are all insignificant, implying that there is no clear time trend in the players’ choices in the second half of the session.[1] Second,consistent with the findings in the literature on gender differences in risk aversion (e.g. Sapienza et al., 2009), female subjects are generally more risk-averse than their male counterparts. On average, female subjects made 1.4 more Safe choices per round than male subjects, and the difference is statistically significant.
D.Certainty Equivalence
To complement our analysis of the number of Safe choices, we createdand computedone additional dependent variable, CE (certainty equivalence), to check the robustness of our results. Suppose that in a round of the set M lotteries in the last six rounds, a rational individual chooses the lottery for any, and the sure outcome for any . If , let ; if k=0, let ; if k=13, let . Therefore, CE indicates the expected certainty equivalence of the lottery for the individual.[2] Analysis of certainty equivalenceis commonly used in the literature (e.g. Goeree et al., 2002, 2003). Again, we focus on subjects’ “rational” decisionsin the second half of the main task (with moderate-variance lotteries).
In TablesA1 and A2, the dependent variable is the natural logarithm of CE.[3]Otherwise, the specifications of the regression models exactly follow those in Tables 5 and 6.In Table A1, the coefficients of PriorRisk are negatively significant, implying that previous exposure to higher risk reduces the subsequent evaluation of certainty equivalence for lotteries. Consistent with the results in Table 6, in Table A2, the coefficients of High in columns (1) and (2) and the coefficients of HM in columns (3) and (4) are negative and statistically significant. Moreover, F tests reject the hypothesis that HM and LM (LM) have equal coefficients with p values <0.1 (<0.02).
Table A1: Effects of previous exposure to risk on certainty equivalence
Notes: Observations that are in rounds 7-12 and have one unique switch point are included. Column (1) regresses ln(Certainty Equivalence) on PriorRisk, x, and period dummy variables. Column (2) includes demographic variables. Column (3) further includes dummy variables of Morerows and Lessrows. Column (4) replaces the period dummies with Last-3, and includes the interaction term between PriorRisk and Last-3. Standard errors clustered at the individual level are reported in parentheses. *, **, and *** represent significance at 10%, 5%, and 1% levels, respectively.
Table A2: Asymmetric effects of previous exposure to risk on certainty equivalence
Notes: Observations that are in rounds 7-12 and have one unique switch point are included. Column (1) regresses ln(Certainty Equivalence) on High, Low, x, and period dummy variables. Column (2) includes demographic variables. Columns (3) and (4) repeat regressions in (1) and (2) while decomposing High and Low to HM, HM', LM and LM'. Standard errors clustered at the individual level are reported in parentheses. *, **, and *** represent significance at 10%, 5%, and 1% levels, respectively.
1
[1]Adding interaction terms between period dummies and PriorRisk to the first three columnsdoes not change the results qualitatively. Meanwhile, most of the coefficients of the period dummies and these interaction terms are statistically insignificant.
[2] The mean and standard deviation of CE are 176.5 and 36.3 respectively for the last six rounds.
[3] Using CE as the dependent variable instead does not change the regression results qualitatively.